World ‘o’ and word ‘O’

There exist two different and separated worlds, ‘o’ and ‘O’ where physical laws uphold.
In each world a measuring rod, made from one atom of Hydrogen that enables the measure by comparison of masses, lengths and time interval.

To keep it simple we will accept that only Hydrogen exists on both. As it is a conceptual experiment we must accept, although impossible, that the observers are made of H.

The difference between worlds is that atoms at ‘O’ are greater than at ‘o’. Observers at ‘o’ and at ‘O’ with their respective measuring rods find the same physical laws.

The observer at ‘o’ see the light emitted at ‘O’ and find that it as the same pattern characteristic of Hydrogen but, and it is a surprise, it is reddened.

The observer at ‘o’ stays undecided between 3 conclusions:

the world ‘O’ is equal to the world ‘o’, but moving away (i.e. it doesn’t recognize the existence of ‘O’)

the world ‘O’ is different

the world ‘O’ is different and moving

The pertinent question is: How to discriminate between the hypotheses?

If world O is moving away from o then as well as redshift events should be seen to happen more slowly.

The reddening itself, wathever its origin, is equivalent to 'happen more slowly' in the 'o' clock units.
With a known message (amplitude and time duration like SN explosion pattern - supose it can happen in a world 'o' and 'O' of H) under what conditions can he distinguish between the 3 answers?

The observer at ‘o’ must validate the physical meaning the hypothesis 2 (and 3).
It has to search for the answer to: can physical laws uphold in a different world O?
Does he have an answer?

Lets explore this situation to make clear what this
"world ‘o’ and world ‘O’" could signify.

I will remember here a book of our childhood :Gulliver and the Liliputians (it happened that Gulliver went to the world of Liliput where liliputians are much smaller than Gulliver)
Lets assume that Gulliver has the same number of atoms, molecules and living cells as the liliputians.
And what the story forget to tell us is that Gulliver had in his pocket a white lamp.
When he left the world of liliputians he offered that lamp to the king of the liliputs and after that it remained in the royal museum with this label "Red lamp kindly offered by the legendary Gulliver".
The liliputians went on with an evolved technical civilization, and many years later one of museum curators analysed the lamp with a spectrometer and he found an amazing fact: The Red Lamp has the same spectrum as his White lamp, but redshifted.
How is it possible ? Simple explanation : on the magic world of our childhood anything is possible. But it makes me think that there must be some kind of enlightment on this story.

I thought you had a question. It looks like you are instead trying to push your own original research, and while waiting for moderator approval, tried to sneak it in the back way.

I quote from you : "I thought you had a question" : the Bohr atom question.

It is a rather evolved question, inteligent and it required some effort to devise how can things be in the way that invalidates those lines of thought of the Gulliver world.

It is not my research as you say. I do not deny that I am familiar with this thinkings for almost 20 years, as I've already said in another post in this forum.
And I had a prompt and correct answer to your question. I think that you will be glad to know the answer.

I've found the BAUT question because in some post in this forum I've found that things are in discussion there. I had to jump there because thay are asking for answers like you did.

In this forum I know that there exists the IR forum but I could not post there just and just because I'm not the author.
I was waiting some changes in the rules in PF (I've heard of some chance of happening) and honestly I like this forum (your intelligent question for example appears in PF not in BAUT).
But life brings surprises to everyone, even to me.

How could I have answered to your question without put the lines in between?

Of course that I know that the conceptual experiment is challenging. But afterall aren't we all in PF to challenge what we know and exchanging knowledge? I think that you became more richer with my answer. You pay nothing and I receive nothing. You can ignore the answer. The post or thread can be blocked or erased or whatever the mentors had to decide. They are observing.

But did you noticed something out of simple physics, a 'mainstream' physics of past ?

'mainstream' = 'fashion' i.e. what we hear or read today.
Solid rock physics of the past is never out of fashion.

I'm here also to learn. I've a lot to learn, and I'm counting on you and many others.
Let it be.